I don't know how to word this so let me explain:

Say your hand is a ship, first off place your hand as if you are placing it on top of a book like how a President Pledges fealty.

Now turn your hand to the side as if you are about to clap.

Using that metaphor, how do I turn my ship around like that in Wing Commander 1?

And can it be done in the later games and the X-Wing games?

You mean roll?
Just hold button 2 on the joystick/gamepad this way you will roll instead of turn while using the X axis (and throttle up/down while using the y axis).

If you ever reply this is the exact flightstick I am using,

https://images-na.ssl-images-amazon.com/images/I/414X2Z0A7TL._SX425_.jpg

works right out of the books but other than the trigger to fire the other buttons don't work I think, but I will check again

Button 2 apart from switching axis and point at the ship in the targeting reticle does literally *nothing* unless you double click it (then it launches missiles).
That stick has a mapping software on the Logitech site (windows only), if really only the trigger works you can create a profile with it that assigns the buttons and the unused axis on the stick to keyboard commands.
If you are on a mac try to see if there are joystick settings for the emulator, Dosbox normally emulates a 4 button stick and Wing Commander should support two buttons out of the box, remember that for these games "button 2" isn't necessarily the same as in windows, so try to hold every button while moving to see if it's the right one.

Turns out that on that Flightstick button 2 is on the thumb button on the stick itself and it helps me roll a ship to its sides.

And it works for other games like X-Wing.

Anyway I also have another question, locking on enemy fighters and missles, how do I make the missles follow the enemy? I noticed that only one time a circle comes to the square target icon and I think that is how to make the missles home in on enemy ships?

Some missiles are dumbfire (they don't lock on targets), others are imrec or image recognition (they lock on the "image" of the target) others are heat seeking (they need to be pointed at the engines of the target to lock on).